关于Hardy-Hilbert不等式的一个改进  

A REFINEMENT ON HARDY-HILBERT’S INEQUALITY

作　　者：高明哲[1] 贾维剑[1] 高雪梅[1] 

机构地区：[1]吉首大学师范学院数学与计算机科学系,湖南吉首416000

出　　处：《数学杂志》2006年第6期647-651,共5页Journal of Mathematics

摘　　要：本文研究关于重级数型Hardy-Hilbert不等式改进的问题.引入可变单位向量的概念,利用Gram矩阵的正定性创建了一个新的不等式.借助于Euler-Maclaurin求和公式,得到了Hardy-Hilbert不等式的结果.当p=2时,给出了经典的Hilbert重级数定理的一个改进.This paper deals with the problem of which the Hardy-Hilbert inequality for double series is refined. A concept of a variable unit-vector is introduced. A new inequality is built by means of the positive definiteness of Gram matrix. And a sharp result of Hardy-Hilbert＇s inequality is obtained with the help of Euler-Maclaurin summation. In particular, for the case p=2, an improvement of the classical Hilbert double series theorem is given.

关 键 词：HARDY-HILBERT不等式 重级数 可变单位向量 GRAM矩阵 泛函分析 

分 类 号：O178[理学—数学]